It is generally recognized that the stick-slip motion of a polycrystalline diamond compact (PDC) bit is responsible for the low rate of penetration (ROP) and premature failure of the PDC bit when drilling in hard rock formations. To solve this problem, a torsional vibration damping tool was developed. A working principle model of the tool and a calculation model of the optimal spiral angle of the tool was established. The stability of the tool was analyzed, and the parameter range of spiral guideline thread stability was determined. The analysis revealed that the tool can automatically adjust the weight on the bit (WOB) and the rotary speed of the PDC bit through the spiral guide and the disc spring, which could suppress the torsional vibration of the PDC bit and convert part of the vibration load into cutting torque for rock breaking and thus to improve the rate of penetration (ROP). The optimal spiral angle of the tool is proportional to the axial stiffiless, bit diameter, and rock hardness of the drill string system and inversely proportional to the torsional stiffness of the drill string system and the reclining angle of the PDC bit. The stability of the tool is related to the spiral angle, length, and friction angle of the spiral guide. The tools were applied in test wells, and the results indicate that the torque fluctuations are significantly decreased and effectively extend the service life of the PDC bit. During the test process, the tool exhibits steady performance, the feasibility of the tool calculation model was verified. It is anticipated that the presented results will make such drilling a more feasible method for well services.